Wyze thermostat wiring at hvac

On my hvac, I have 2 cables. One I believe goes to ac unit (2 wires), the other goes to the thermostat control (5+ wires). The control is not using the c wire even though it is connected to the hvac board. I couldn’t get the thermostat to work using the c wire so I used the adapter in place of it. My question is about the cable with the 2 wires (again I think it goes to ac unit), it was attached to 2 contacts on the hvac board (shared with the c/y wire from the thermostat control)- to the Y wire and the C wire. Do I connect it back to to the hvac board? Leave them off? Connect them to the C wire adapter?

Leave the wires going to the ac compressor where they are, unless you want the air conditioner to turn on every time the heat turns on. (You do not want this)

You really don’t need the adapter since you have a C wire. Post a picture of your wiring at the thermostat

The picture is misleading cus it looks like there are 2 set of wires connected to the board. The red and white is one and the rest which seems typical is the other. I agree post pic of the wiring at the old thermostat.